The following publications are cited as reference to the prior art:
USA patents: PA1 Scientific papers:
[p1] U.S. Pat. No. 4,257,274 (Shimada et al ) PA0 [p2] U.S. Pat. No. 4,386,453 (Gianchino et al.) PA0 [p3] U.S. Pat. No. 4,332,000 (Petersen), PA0 [p4] U.S. Pat. No. 4,390,925 (Freud) PA0 [p5] U.S. Pat. No. 3,397,278 (Pomerantz) PA0 [p6] U.S. Pat. No. 4,589,054 (Kuisma) PA0 [p7] U.S. Pat. No. 4,628,403 (Kuisma) PA0 [p8] U.S. Pat. No. 4,594,639 (Kuisma) PA0 [p9] U.S. Pat. No. 4,83 1,492 (Kuisma) PA0 [p10] U.S. Pat. No. 4,996,627 (Zias et at.) PA0 [p11] U.S. Pat. No. 5,019,783 (Cadwell) PA0 [p12] U.S. Pat. No. 5,028,876 (Cadwell) PA0 [p13] U.S. Pat. No. 5,048,165 (Cadwell) PA0 [p14] U.S. Pat. No. 4,679,434 (Stewart) PA0 [p15] U.S. Pat. No. 5,095,750 (Suzuki et al.) PA0 [a1] K. Warren, Navigation 38, 91 (1991). PA0 [a2] K. D. Wise, in Proceedings of the Workshop Advances in Analogue Circuit Design, Katholieke Universiteit Leuven, April 1993. PA0 [a3] Y. de Coulon et al., Design and Test of a Precision Servoaccelerometer with Digital Output, The Proceedings of the 7th International Conference on Solid-State Sensors and Actuators, pp. 832-835, 1993.
Cited publications [p1-p10] describe capacitive pressure transducer structures in which the silicon diaphragm acting as the transducing electrode is flexible relative to a rigid metal electrode. Cited patents [p1, p10] disclose particularly a transducer structure suited for measuring the pressure difference imposed on the transducer diaphragm by the pressures acting on the different sides of the diaphragm. Such a transducer structure is termed a differential pressure transducer.
Prior-art differential pressure transducer constructs can be divided into asymmetrical and symmetrical structures. In an asymmetrical structure [cf. p1, p8], the capacitance change is measured only between the pressure-sensitive diaphragm and a single metal electrode. In a symmetrical structure [cf. p1, p4, p10], the capacitance measurement is performed between the pressure-sensitive diaphragm and metal electrodes placed on both sides of the diaphragm, which arrangement renders differential capacitance measurement possible.
In structures based on the flexure of the pressure-sensitive diaphragm under pressure, temperature dependence is approximately a linear function of the deflection of the diaphragm. A major portion of the temperature dependence in a symmetrical differential pressure transducer structure is constituted by the difference of the thermal expansion constants of the silicon diaphragm and the substrate.
The measurement circuit in which the differential pressure transducer is employed is based on conventional capacitance measurement. Numerous measurement techniques are known. In a measurement circuit employing a symmetrical differential pressure transducer, a transfer function is obtained which is proportional to differential capacitance. A benefit thereof is that a vastly improved linearity results about the zero point in relation to an asymmetric transducer structure.
The literature of the art recognizes measurement systems for silicon micromechanical structures [cf. p14, p15, al ] based on the force equilibrium principle. The mechanical force acting on the transducer is compensated by an electrostatically controllable force. The mutual force of attraction generated by an electric field between two electrodes can be computed from the equation: ##EQU1## where U is the electrical potential difference between the electrodes, d is the distance between the electrodes, dA is an infinitesimal area element of the electrode surface and .epsilon..sub.O .epsilon..sub.r is the dielectric constant of the insulating medium. Characteristically, the voltage-force transfer function is nonlinear relative to the feedback voltage. However, in a symmetrical structure the transfer function can in principle be linearized using two different techniques. When the metal electrodes 74 are biased as illustrated in FIG. 7b by applied voltages 72 (V.sub.bias) and 73 (-V.sub.bias) and a feedback voltage 71 (V) is applied to the center electrode 75, the resulting electrostatic net force is ##EQU2##
The voltage applied to the center electrode 75 is taken to a preamplifier for further processing. High-pass filtering of the measurement signal is provided by an RC circuit 78.
An alternative possibility illustrated in FIG. 7a is to connect the bias voltages 72 (V.sub.bias) and 73 (-V.sub.bias) to the metal electrodes 74, then to sum the electrostatic force feedback voltage 71 (V) to the electrodes, and to take the center electrode 75 to ground potential via a resistor 77. The outcome is exactly the same as in the first arrangement: the electrostatically imposed force is a linear function of the voltage applied between the electrodes. The output voltage of the preamplifier 76 is taken to a feedback circuit (not shown). The feedback circuit is configured to control the output voltage to zero.
The electrostatic feedback force can also be generated by means of a pulsed voltage. If the pulse rate of the applied voltage is essentially above the transducer dynamic response cutoff frequency (that is, the lowest natural frequency of the transducer), the transducing electrode is subjected to an average electrostatic force ##EQU3## where U.sub.pulse is the pulse amplitude, T.sub.pulse is the pulse width and f.sub.pulse is the frequency (repetition rate) of the pulsed control voltage. The electrostatic feedback force can then be controlled by the pulse amplitude, width and/or rate. When using constant-amplitude pulses with either pulse-width or pulse-rate modulation, a linear relationship is obtained between the pulse width or rate and the average electrostatic force [cf. a3, p15]. The feedback arrangement for the transducer according to the invention can be implemented using either a DC voltage or a pulsed voltage. Feedback by means of a pulsed control voltage is particularly applicable to asymmetric structures facilitating a linear transfer function.
Electrostatic force feedback has been applied to measurement circuits built around micromechanical acceleration transducers. The same principle can be employed in measurement circuits built around differential pressure transducers. For a symmetrical transducer controlled to the force equilibrium, the output voltage is ##EQU4## where .DELTA.p is the differential pressure acting across the diaphragm and g is the gap distance between the electrodes. If a control voltage span of .+-.10 V is available and a differential pressure measurement range of .+-.500 Pa is desired, the mutual distance between the electrodes shall be 2 .mu.m or less. In practice, such small dimensions required and the narrow differential pressure range available have curtailed the application of an electrostatic force feedback-controlled differential pressure transducer. However, a differential pressure transducer based on controlled force equilibrium excels by its linearity and low temperature dependence, since the diaphragm profile can be kept unflexed by virtue of the applied feedback.
The above-given equation is, however, only valid for an ideal transducer structure namely, the mutual distances of the transducer pressure-sensitive diaphragm 75 to both electrodes 74 must be equal. If the mutual distances of diaphragm to the electrodes are unequal, the result is that the zero position of the difference capacitance .DELTA.C=C.sub.1 -C.sub.2 does not coincide with the unflexed position of the transducer diaphragm. Any deviation from the ideal condition causes higher temperature dependence and nonlinearity of the transducer.
In a feedback-controlled micromechanical transducer, two separate metal electrodes are preferably used: a first electrode for feedback and a second electrode for capacitance measurement [cf. p15, a2]. This arrangement aims at a more straightforward measurement circuitry by virtue of separating the feedback voltage and the measurement signal from each other.